Question

How many times, the potential of big drop in comparison to small drops which is made of $8$ droplets will be, if all the droplets are identical?

• A. 2 times
• B. 4 times
• C. 3 times
• D. 8 times

Answer 1

Answer: (B)

Volume of bigger drop $=8 \times$ volume of small drops
$ \frac{4}{3} \pi R^{3} =8 \times \frac{4}{3} \pi r^{3} $
$ R =2 r $
Potential on small drop $V_{1}=\frac{1}{4 \pi \varepsilon_{0}} \frac{q}{r}$
Potential on bigger drop
$V_{2} =\frac{1}{4 \pi \varepsilon_{0}} \frac{8 q}{R} $
$=\frac{1}{4 \pi \varepsilon_{0}} \frac{8 q}{2 r} $
$=4\left(\frac{1}{4 \pi \varepsilon_{0}} \frac{q}{r}\right)$
$=4 V_{1}$
So, potential on the bigger is four times to that potential on small.